Model glasses coupled to two different heat baths

TL;DR

This paper develops a two-temperature thermodynamics for a spin-glass model with spins and couplings coupled to separate heat baths, revealing novel phase transitions and non-equilibrium effects.

Contribution

It introduces a generalized thermodynamics framework for spin glasses with coupled heat baths, including a replica theory with a non-zero replica number and analysis of phase transitions.

Findings

Existence of two distinct glassy phases at low temperatures for p>2.

First-order transitions with positive latent heat and entropy discontinuity.

Removal of marginal stability in the p=2 case due to disorder correlation.

Abstract

In a $p$-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change in the course of time. The spins are coupled to a heat bath with temperature $T$, while the coupling constants are coupled to a bath having temperature $T_{J}$. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, $n=T/T_J$. For $p>2$ there occur at low temperatures two different glassy phases, depending on the value of $n$. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is the essentially non-equilibrium effect. The predictions of longtime dynamics and infinite-time statics differ only for $n<1$ and $p>2$. For $p=2$ correlation of the disorder (leading to a non-zero $n$) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the broken-ergodicity dynamics in the usual spin-glass models and non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived.